This invention relates to apparatus for and a method of operating Coriolis flowmeters over an extended temperature range that includes cryogenic temperatures. More particularly, the invention provides apparatus for and a method of generating accurate output temperature compensated flow information by a Coriolis flowmeter operated at cryogenic temperatures.
It is known to use Coriolis effect mass flowmeters to measure mass flow and other information pertaining to a material flow as disclosed in U.S. Pat. No. 4,491,025 issued to J. E. Smith, et al. of Jan. 1, 1985 and Re. 31,450 to J. E. Smith of Feb. 11, 1982. These flowmeters have one or more flow tubes of a straight or curved configuration. Each flow tube configuration has a set of natural vibration modes, which may be of a simple bending, torsional, radial, or coupled type. Each flow tube is driven to oscillate at resonance in one of these natural modes. The natural vibration modes of the vibrating, material filled Coriolis flowmeter system are defined in part by the combined mass of the flow tubes and the material within the flow tubes. Material flows into the flowmeter from a connected material source on the inlet side of the flowmeter. The material is then directed through the flow tube or flow tubes and exits the flowmeter to a material destination connected on the outlet side of the flowmeter.
A driver applies a vibrational force to the flow tube to cause the flow tube to oscillate. When there is no material flowing through the flowmeter, all points along a flow tube oscillate with an identical phase. As a material begins to flow, Coriolis accelerations cause each point along the flow tube to have a different phase with respect to other points along the flow tube. The phase on the inlet side of the flow tube lags the driver, while the phase on the outlet side leads the driver. Sensors are placed at two different points on the flow tube to produce sinusoidal signals representative of the motion of the flow tube at the two points. A phase difference of the signals received from the two sensors is calculated in units of time. The phase difference between the two signals is proportional to the mass flow rate of the material flowing through the flow tube or flow tubes.
Coriolis flowmeters are in wide spread use that generated accurate information regarding material flow. This information includes material mass flow rate as well as material density. Coriolis flowmeters range in size from those having a flow tube diameter of 0.16 centimeters to those having a diameter of 15 centimeters. These flowmeters serve a wide range of material flow rates ranging from approximately several drops per minute, such as for use in anesthesiology systems, to several tons a minute, such as those used in oil pipelines or for the loading and unloading of oil tankers. Regardless of size, most of the applications in which Coriolis flowmeters are used require a high degree of accuracy such as, a maximum error of 0.10%. This accuracy can be achieved by many of the currently available Coriolis flowmeters provided they are operated at the conditions for which each flowmeter is designed.
Operating temperature is a condition of paramount concern to a Coriolis flowmeter. A typical range of operating temperatures for a Coriolis flowmeter is approximately 33 k to 473 k (xe2x88x92240xc2x0 C. to +200xc2x0 C.). In designing a Coriolis flowmeter to generate accurate output information under this temperature range, the thermal stresses generated within the Coriolis flowmeter as well as temperature differentials between the internal parts of the Coriolis flowmeter must be considered. The design must include a consideration of the thermal expansion/contraction of the various parts of the Coriolis flowmeter to prevent damage to these parts as well as to compensate for the affect this thermal expansion/contraction may have on the output accuracy of the flowmeter.
The output data of a Coriolis flowmeter that is of great importance is the mass flow rate since the accuracy of most data generated by the Coriolis flowmeter is dependent upon the accuracy of the mass flow rate. The accuracy of the mass flow rate is dependent upon the accuracy of the Young""s Modulus E term used in the mass flow rate determination. An accurate determination of mass flow rate requires that Young""s Modulus E be determined with precision over the temperature range in which the Coriolis flowmeter operates. It is often assumed that the Young""s Modulus E variation with temperature is linear over the temperature range with which the Coriolis flowmeter operates. Therefore, Young""s Modulus E is typically calculated using a linear expression containing a temperature term T representing the measured temperature of the Coriolis flowmeter. This linear expression for E is then used to determine the mass flow rate.
The above assumptions are satisfactory for temperature ranges for which Young""s Modulus E varies linearly with temperature. However, the above assumptions are not useful in determining Young""s Modulus E at cryogenic temperatures (those below 273 k). It is known from an article by HM Ledbetter from the Journal of Applied Physics of March 1981 that the Young""s Modulus E for stainless steel varies linearly over a range of approximately 100 k to 300 k and higher; but has a non-linear variation at cryogenic temperatures, such as those below 100 k.
The use of an assumed linear variation of E at cryogenic temperatures results in a calculation of Young""s Modulus E that has an unacceptable accuracy. The use of a linear expression for Young""s Modulus E at cryogenic temperatures requires that the calculated Young""s Modulus E be altered by an arbitrary amount for each different cryogenic temperature to determine Young""s Modulus E and, in turn, the mass flow rate of the Coriolis flowmeter with a satisfactory accuracy. This procedure however, is cumbersome and is limited to a small number of predetermined temperatures.
The above and other problems are solved and an advance in the art is achieved by the apparatus and method of the present invention which calculates Young""s Modulus E with accuracy over the conventional range of the conventional temperature range of xe2x88x92100xc2x0 C. to +200xc2x0 C. as well as at cryogenic temperatures below xe2x88x92100xc2x0 C. and down to xe2x88x92269xc2x0 C.
The apparatus and method of the present invention involves the steps of calculating Young""s Modulus E for a wide range of temperatures ranging from 4 k to 473 k. It does this by applying non-linear curve fitting to priorly measured data representing Young""s Modulus E for the temperature range of interest. This provides a non-linear expression characterizing Young""s Modulus E over this temperature range. This non-linear expression is then used in the mass flow rate calculation to generate an accurate mass flow rate.
The step of subjecting a range of measured values of Young""s Modulus E to non-linear curve fitting may involve deriving a plurality of expressions for Young""s Modulus E including a linear expression as well as expressions of the second, third, and fourth order, or higher orders. The expression for each order is unique. The first order linear expression contains a term of T. The second order expression contains the terms T2 and T. The third expression contains terms T3, T2, and T. The fourth order expression contains the terms T4, T3, T2, and T. These expressions are evaluated compared to determine the accuracy of the output data each generates. The expression of the lowest order that yields the desired accuracy is used. It was found that Young""s Modulus E expression becomes increasingly accurate for the higher order expressions for cryogenic temperatures. All expressions generate a Young""s Modulus E having an accuracy of at least 0.15% down to an approximately xe2x88x92100xc2x0 C. Below that temperature, the error for the first order linear curve fit increases exponentially to an unacceptable level of more than 5% error. The second order expression containing T2 and T produces acceptable results down to approximately xe2x88x92150xc2x0 C. Below that, its error increases exponentially up to more than 3%. The third order expression containing T3, T2, and T has an acceptable error rate down to approximately xe2x88x92200xc2x0 C. Its error rate increases exponentially for temperatures below xe2x88x92200xc2x0 C. The fourth order expression has an acceptable error rate down to approximately xe2x88x92200xc2x0 C. and then increases to an error rate of approximately 1.5% for lower temperatures.
In summary, the apparatus and method of the present invention uses measured values of Young""s Modulus E, subjects them to curved fitting operations that generate a linear first order linear expression as well as higher order non-linear expressions. These expressions are used for the Young""s Modulus E term in the calculation used to determine the mass flow rate. Each expression is advantageous for a unique range of Coriolis flowmeter operating temperatures. The first order linear expression produces acceptable accuracy for limited range of operating temperatures. The second order expression produces acceptable results for a wider range of operating temperatures. The third and fourth order expressions each are advantageous for increased ranges of operating temperatures.
Aspects
An aspect of the invention includes a Coriolis flowmeter having a fluid flow to derive non-linear temperature compensated output information, said method comprising:
measuring the operating temperature T of a flow tube means of said Coriolis flowmeter,
storing non-linear temperature compensation information for material embodying said flow tube means,
defining an expression relating said operating temperature T to said non-linear temperature compensation information, and
solving said defined expression to generate non-linear temperature compensated fluid flow output information for said Coriolis flowmeter at said operating temperature T.
Preferably said step of solving said defined expression includes the step of determining a non-linear temperature compensated mass flow rate {dot over (M)} for the fluid flow in said Coriolis flowmeter.
Preferably said operating temperature T is measured and stored in a memory of said meter electronics.
Preferably storing said non-linear temperature compensation information in said memory; and
reading said non-linear temperature compensation information out of said memory for use in said defined expression to generate non-linear temperature compensated fluid flow output information for said Coriolis flowmeter at said operating temperature.
Preferably said non-linear temperature compensation information comprises the step of storing measured values of Young""s Modulus E for a predetermined range of temperatures of said material embodying said flow tube means.
Preferably said non-linear temperature compensation information includes the step of storing measured values of Young""s Modulus E for a predetermined range of temperatures of said material embodying flow tube means, said method further includes the steps of:
determining E for said operating temperature T, and
using said determined E in said defined expression that is solved to generate said non-linear temperature compensated fluid flow output information.
Preferably said defined expression includes the step of determining a non-linear temperature compensated mass flow rate {dot over (M)} for the fluid flow in said Coriolis flowmeter.
Preferably said step of using said determined E includes the steps of:
using said operating temperature T to access the location of said memory that stores the value of E corresponding to said operating temperature T, and
reading said value of E from said memory for use in solving said defined expression.
Preferably said Coriolis flowmeter includes: a method and apparatus that reads the value of E from said accessed location when said operating temperature T corresponds to a location in said memory;
determining that a received value of T does not correspond to a location in said memory;
determining the location in said memory corresponding to a value of T that is the closest to said received value of T; and
determining a value of E for said received value of T by interpolating of the value of E for said location having a value of T that is the closest to said received value of T and that using said interpolated value of T in said defined expression that is solved to generate said non-linear temperature compensated fluid flow output information.
Preferably said step of solving:
obtaining a non-linear expression for said non-linear temperature compensation information as a function of T, and
using said non-linear expression for said non-linear temperature compensation information in said defined expression to generate non-linear temperature compensated fluid flow output information for said Coriolis flowmeter.
Preferably said steps of obtain and using inludes the steps of:
obtaining a non-linear expression for Young""s Modulus E as a function of T, and
using said non-linear expression for Young""s Modulus E in said defined expression to generate non-linear temperature compensated fluid flow output information for said Coriolis flowmeter.
Preferably said step of determining said non-linear temperature compensated flow output information includes the step of determining a non-linear temperature compensated mass flow rate {dot over (M)} for said fluid flow.
Preferably said non-linear temperature compensation information information for said material embodying said flow tube means includes measured values of Young""s Modulus E for a plurality of measured operating temperatures T of said flow tube means; said meter electronics:
curve fitting said measured values of E to obtain said non-linear expression for E expressed as a function of T, and
using said non-linear expression for Young""s modulus E in said defined expression to generate said non-linear temperature compensated fluid flow output information for said Coriolis flowmeter.
Preferably said measured values of E are stored in a memory of Coriolis flowmeter.
Preferably said meter electronics receives said operating temperature T and applies said operating temperature T to said expression to generate said non-linear temperature compensated fluid flow output information.
Preferably said step of curve fitting performs an n order curve fit for said values of Young""s Modulus E to generate an equation for determining said temperature compensation output information wherein n is greater than 1.
Preferably said step of curve fitting performs a second order curve fit for said values of Young""s Modulus E for use said expression for determining said non-linear temperature compensated fluid flow output information for said Coriolis flowmeter.
Preferably said step of curve fitting performs a third order curve fit for said values of Young""s Modulus E for use said expression for determining said non-linear temperature compensated fluid flow output information for said Coriolis flowmeter.
Preferably said step of curve fitting performs a fourth order curve fit for said values of Young""s Modulus E for use in said expression for determining said non-linear temperature compensated fluid flow output information for said Coriolis flowmeter.
Preferably said step of curve fitting performs a fifth order curve fit for said values of Young""s Modulus E for use in said expression for determining said non-linear temperature compensated fluid flow output information for said Coriolis flowmeter.
Preferably the step of receiving fluid flow output information that embodies linear temperature compensation for Young""s Modulus E of said material embodying the flow tube means of said Coriolis flowmeter;
receiving the operating temperature T of said Coriolis flowmeter;
removing said linear temperature compensation from said output information of said Coriolis flowmeter to provide an uncompensated fluid output flow information for said Coriolis flowmeter;
using said defined expression relating said operating temperature T and to said non-linear temperature compensation information, and
solving said defined expression to generate non-linear temperature compensated fluid flow output information for said Coriolis flowmeter at said operating temperature T.
Preferably said stored non-linear temperature compensation information for said material embodying said flow tube means includes a plurality of non-linear expressions for Young""s Modulus E expressed as a function of operating temperature T, said meter electronics;
receiving said operating temperature T;
using said received operating temperature T to select one of said plurality of non-linear expressions; and
using said selected non-linear expression for Young""s module E in said defined expression to generate said non-linear temperature compensated flow output information for said Coriolis flowmeter.
Another aspect of the invention is a flow tube means adapted to be vibrated while receiving a fluid flow,
meter electronics that receives signals from pick offs coupled to said vibrating flow tube means,
said signals indicating a phase difference between two points on said flow tube means to which said pick offs are coupled,
said meter electronics also receives signals indicating an operating temperature T of said flow tube means from a temperature sensor,
said meter electronics comprising:
compensation circuitry that relates said operating temperature T to non-linear temperature compensation information for said material embodying flow tube means, and
circuitry that receives said non-linear temperature compensation information, receives said pick offs signals, and applies said non-linear temperature compensation information to generate non-linear temperature compensated fluid flow output information for said Coriolis flowmeter.
Preferably said fluid flow output information includes a non-linear temperature compensated mass flow rate {dot over (M )} of said material flow.
Preferably said operating temperature T is measured and stored in a memory of said meter electronics.
Preferably said non-linear temperature compensation information for a plurality of operating temperatures is stored in a memory of said meter electronics:
said meter electronics further comprising look-up circuitry that reads said temperature compensation information for said operating temperature T from said memory for use in said defined expression to generate non-linear temperature compensated fluid flow output information for said Coriolis flowmeter.
Preferably said non-linear temperature compensation information comprises measured values of Young""s modulus E for a predetermined range of temperatures of said material embodying said flow tube means.
Preferably said non-linear temperature compensation information includes measured values of Young""s modulus E for a predetermined range of temperatures of said flow tube means, said meter electronics further includes:
apparatus that generates Young""s modulus E for said operating temperature T, and
apparatus that uses said determined Young""s modulus E in said defined expression that is solved to generate said non-linear temperature compensated fluid flow output information.
Preferably said fluid flow output information includes the non-linear temperature compensated mass flow rate {dot over (M )} or said fluid flow in said Coriolis flowmeter.
Preferably said Coriolis flowmeter includes:
apparatus that uses said operating temperature T to access the location of said memory storing the value of Young""s modulus E corresponding to said operating temperature T, and
apparatus that reads said value of Young""s modulus E from said memory for use in solving said defined expression.
Preferably said apparatus includes: apparatus that reads the value of E from said accessed location when said operating temperature T corresponds to a location in said memory;
apparatus that determines when a received value of T does not correspond to a location in said memory;
apparatus that determines the location in said memory corresponding to a value of T that is the closest to said received value of T;
apparatus that determines a value of E for said received value of T by interpolating of the value of E for said location having a value of T that is the closest to said received value of T and that uses said interpolated value of T in said defined expression that is solved to generate said non-linear temperature compensated fluid flow output information.
Preferably said meter electronics comprises:
apparatus that stores a non-linear expression for said non-linear temperature compensation information as a function of T, and
apparatus that uses said non-linear expression for said non-linear temperature compensation information in said defined expression to generate non-linear temperature compensated flow output information for said Coriolis flowmeter.
Preferably said meter electronics includes:
apparatus that stores a non-linear expression for Young""s modulus E as a function of T, and
apparatus that uses said non-linear expression for Young""s modulus E in said defined expression to generate non-linear temperature compensated fluid flow output information for said Coriolis flowmeter.
Preferably said apparatus that generates said non-linear temperature compensated flow output information includes apparatus that generates a non-linear temperature compensated mass flow rate {dot over (M )} for said fluid flow.
Preferably said non-linear temperature compensation information includes measured values of Young""s modulus E for a range of operating temperatures; said meter electronics further includes;
apparatus that curves fits said measured values of E to obtain said non-linear expression for E expressed as a function of T, and
apparatus that uses said non-linear expression for E in said defined expression to generate said non-linear temperature compensated fluid flow output information for said Coriolis flowmeter.
Preferably said measured values of E are stored in a memory of said meter electronics.
Preferably the meter electronics further comprises:
application circuitry in said meter electronics that receives said operating temperature T and said applies said operating temperature T to said expression to generate said temperature compensation information for use in said defined expression to generate non-linear temperature compensated fluid flow output information for said Coriolis flowmeter.
Preferably the meter electronics further comprises:
apparatus that receives data including Young modulus E for each of a plurality of temperatures and performs an n order curve fit for said values of Young""s modulus E to generate an expression for use in determining said temperature compensation output information wherein n is greater than 1.
Preferably said meter electronics comprises:
circuitry that generates a second order form fit of said values of Young""s modulus E to generate said expression for determining said non-linear temperature compensated fluid flow output information for said Coriolis flowmeter.
Preferably said meter electronics comprises:
circuitry that generates a third order form fit of said values of Young""s modulus E to generate said expression for determining said non-linear temperature compensated fluid flow output information for said Coriolis flowmeter.
Preferably said meter electronics comprises:
circuitry that generates a fourth order form fit of said values of Young""s modulus E to generate said expression for determining said non-linear temperature compensated fluid flow output information for said Coriolis flowmeter.
Preferably said meter electronics comprises circuitry that generates a fifth order form fit of said values of Young""s modulus E to generate said expression for determining said non-linear temperature compensated fluid flow output information for said Coriolis flowmeter.
Preferably the Coriolis flowmeter further includes:
apparatus that receives fluid flow output information containing linear temperature compensation for Young""s modulus E of material embodying a flow tube means of said Coriolis flowmeter;
apparatus that receives the operating temperature T of said Coriolis flowmeter;
apparatus that removes said linear temperature compensation from said output information of said Coriolis flowmeter to provide an uncompensated fluid output flow information for said Coriolis flowmeter;
apparatus that uses said defined expression relating said operating temperature T to said non-linear temperature compensation information, and
apparatus that solves said defined expression to generate non-linear temperature compensated fluid flow output information for said Coriolis flowmeter at said operating temperature T.
Preferably said stored non-linear temperature compensation information includes a plurality of non-linear expressions for Young""s Modulus E expressed as a function of operating temperature T, said meter electronics further includes;
apparatus said receives said operating temperature T;
apparatus that uses said received operating temperature T to select one of said plurality of non-linear expressions;
apparatus that uses said selected non-linear expression for E in said defined expression to generate said non-linear temperature compensated flow output information for said Coriolis flowmeter.